Satellite motion around Earth is represented by computing about 120 orbital parameters, put into 28 groups. The number is large, because some parameters are computed using more than one model equation, that require different inputs. This confirms accuracy & validation of results and understanding the different input considerations.

Satellite is an artificial object, intentionally placed into orbit. Thousands of Satellites have been launched into orbit around Earth. A few Satellites called Space Probes have been placed into orbit around Moon, Mercury, Venus, Mars, Jupiter, Saturn, etc. The Moon is the Earth’s only natural Satellite, moves around Earth in the same kind of orbit.

The Motion of a Satellite is a direct consequence of the Gravity of a body (earth), around which the satellite travels without any propulsion. A satellite move around Earth is pulled in by the gravitational force (centripetal) of the Earth. Contrary to this pull, the rotating motion of satellite around Earth has an associated force (centrifugal) which pushes it away from the Earth. The centrifugal force equals the gravitational force and perfectly balance to maintain the satellite in its orbit.

The Velocity of a Satellite in circular or elliptical orbit depends on its altitude ‘h’ at that point. Secondly, the mass of satellite does not appear in its velocity equations. Thus satellite velocity in its orbit is independent of its mass. Further, a satellite in elliptical orbit moves faster when closer to earth (near perigee) and moves slower when farther from earth (near apogee).

Earth Rotates on its axis passing through the North and South Poles. The rotation is counterclockwise looking down at North Pole. This rotation results daytime in area facing Sun and night time in area facing away from Sun. Since we are on Earth, we do not sense its rotation, but experience by observing the relative motion of the Sun (like from a moving vehicle we see the surroundings move).

The time for Earth to make a complete rotation is approximately 24 hours (exactly 23.9344699 hours or 23 hours, 56 minutes, 4.0916 seconds). The earth’s orbit around the sun is not a circle, it is slightly elliptical. Therefore, distance between earth and sun varies throughout the year.

The Position of Earth on celestial sphere is characterized by computing around 120 orbital parameters. The number is large, because some parameters are computed using more than one model equation, that require different inputs. This helps in validation of results and understanding the different input considerations.

The Orbital Parameters that Characterize the Position of Earth on Celestial Sphere, are put into following groups :

Positional Astronomy – Earth Orbit around Sun

Positional Astronomy is measurement of Position and Motion of objects on celestial sphere seen at a particular time and location on Earth. The Positional Astronomy, also called Spherical Astronomy, is a System of Coordinates.

The Earth is our base from which we look into space. Earth orbits around Sun, counterclockwise, in an elliptical orbit once in every 365.26 days. Earth also spins in a counterclockwise direction on its axis once every day. This accounts for Sun, rise in East and set in West. Earth Revolution refers to orbital motion of the Earth around the Sun. Earth axis is tilted about 23.45 deg, with respect to the plane of its orbit, gives four seasons as Spring, Summer, Autumn and Winter.

Moon and artificial Satellites also orbits around Earth, counterclockwise, in the same way as earth orbits around Sun.

In the early 1600s, Johannes Kepler proposed three laws of planetary motion.

First Look at the Preliminaries about ‘Positional Astronomy’, before moving to the computation & predictions of astronomical events.

Time is a dimension in which the events can be ordered from the past through the present into the future. Our clocks are set to run (approximately) on solar time (sun time). For astronomical observations, we need to use sidereal time (star time).

Time Standards and designations : Solar Time, Sidereal Time, Equation of time, Precession, Nutation, Hour Angle HA, GMT, GMST, LMT, LMST, Universal Time UT, International Atomic Time TAI, Ephemeris Time ET, Gregorian calendar, Julian Day JD.

The Precise time conversion utilities :

* Conversion of Universal Time To Julian Day;

* Conversion of Julian Day To Universal Time;

* Conversion of Fundamental Epoch To Julian day and Julian century;

* Add or Subtract time (days, hour, minute seconds) to or from input time;

* Julian day for start of any Year;

* Solar Time : Local Mean Solar Time (LMT) over observer’s Longitude;

* Sidereal Time : Greenwich universal time at hour 0.0 (ST0) and GMST;

Introduction to OM-MSS Software

We look into space from Earth, which is 3rd planet from Sun. Earth takes around 365.25 days to moves around Sun in an Elliptical orbit. The average distance from the Earth to the Sun is called one Astronomical Unit (AU); 1 AU = 149,597,870.7 km. Mars is 4th planet from Sun, that takes 686.971 Earth days to orbit around Sun. The orbital path of Mars is highly eccentric. Mars & Earth move along their orbits, and come near to one another approximately every two years. This approach of coming near facilitate launching of spacecraft every two years, even that takes about eight months to reach Mars. Example : On Apr. 08, 2014, the near or close distance between Mars and Earth was 92.4 million km. Moon moves around Earth in the same kind of orbit. The Moon is the Earth’s only natural Satellite. The average distance of the Moon from the Earth is 384,403 km. A Satellite is an artificial object, intentionally placed into orbit. Thousands of Satellites are launched into orbit around Earth. A few Satellites called Space Probes have been placed into orbit around Moon, Mercury, Venus, Mars, Jupiter, Saturn, etc. Understanding the motion of Earth around Sun, and the motion of Moon and Satellites around Earth is of interest to many.

The OM-MSS is a software that simulates motion of Earth, Moon & Satellites in their respective Orbits with respect to Sun. The Software is written in ‘C’ Language. The Compiler used is Dev C++ and the Platform is a Windows 7, 64 bit Laptop. The Source Code around 30,000 Lines, is Compiled. The ‘OM-MSS.EXE’ File generated is of Size 1.5 KB. The Executable File, < OM-MSS.EXE >, is RUN Step-by-Step for a Set of Inputs. The execution of ‘Orbital Mechanics – Model & Simulation Software (OM-MSS)’, illustrates its Scope, Capability, Accuracy, and Usage. The OM-MSS Software is quite exhaustive for beginners, experts, researchers & professional in Spherical Astronomy. The source code of OM-MSS Software in full or in parts has a cost if there is buyer. The cost has not been evaluated / decided. The OM-MSS Software includes the following :

(a) Astronomical Time Standards and Time Conversions Utilities :

GMT – Greenwich Mean Time, LMT – Local Mean Time, LST – Local Sidereal Time, UT – Universal Time,

The Software is written in ‘C’ Language. The Compiler used is Dev C++ and the Platform is a Windows 7, 64 bit Laptop. The Source Code around 30,000 Lines, is Compiled. The ‘OM-MSS.EXE’ File generated is of Size 1.5 KB. The Executable File, < OM-MSS.EXE >, is RUN Step-by-Step for a Set of Inputs.

The execution of OM- MSS illustrates its Scope, Capability, Accuracy, and Usage.

The Results seen on Computer Screen are put in a File, that in effect becomes :

‘A Monograph of Orbital Mechanics with Examples, Problems and Software Driven Solutions‘, Page 1 – 402, which includes the following :